Journal of Theoretical and Applied Information Technology
© 2007 JATIT. All rights reserved.
www.jatit.org
DIRECT TORQUE CONTROL FOR INDUCTION MOTOR
USING INTELLIGENT TECHNIQUES
R.Toufouti S.Meziane ,H. Benalla
Laboratory of Electrical Engineering University Constantine Algeria
[toufoutidz,mezianedz, Benalladz]@yahoo.fr
ABSTRACT
In this paper, we propose two approach intelligent techniques of improvement of Direct Torque Control
(DTC) of Induction motor such as fuzzy logic (FL) and artificial neural network (ANN), applied in
switching select voltage vector .The comparison with conventional direct torque control (DTC), show that
the use of the DTC_FL and DTC_ANN, reduced the torque, stator flux, and current ripples. The validity
of the proposed methods is confirmed by the simulative results.
Keywords: Fuzzy inference system (FIS); Fuzzy logic, direct torque control (DTC), induction motor,
artificial neural network (ANN).
1. INTRODUCTION
Induction motor drives controlled by Field
Oriented control (FOC) [1] have been till now
employed in high performance industrial
applications, has achieved a quick torque response,
and has been applied in various industrial
applications instead of dc motors [1]-[22].It permit
independent control of the torque and flux by
decoupling the stator current into two orthogonal
components FOC, however, is very sensitive to
flux, which is mainly affected by parameter
variations. It depends on accurate parameter
identification to achieve the expected performance.
During the last decade a new control method
called DTC (Direct Torque Control) has been
developed for electrical machines[1]-[22].TC
principles were first introduced by Depenbrock [1]
and Takahashi [2]. In this method, Stator voltage
vectors is selected according to the differences
between the reference and actual torque and stator
flux linkage. The DTC method is characterised by
its simple implementation and a fast dynamic
response. Furthermore, the inverter is directly
controlled by the algorithm, i.e. a modulation
technique for the inverter is not needed [1][7].However if the control is implemented on a
digital system (which can be considered as a
standard nowadays), the actual values of flux and
torque could cross their boundaries too far. The
main advantages of DTC are absence of
coordinate transformation and current regulator;
absence of separate voltage modulation block,
Common disadvantages of conventional DTC are
high torque ripple and slow transient response to
the step changes in torque during start-up[1]-[4].
For that reason the application of Fuzzy logic and
artificial neural network attracts the attention of
many scientists from all over the world [1]. The
reason for this trend is the many advantages which
the architectures of ANN have over traditional
algorithmic methods [8]-[22]. .
Among the advantages of ANN are the ease of
training and generalization, simple architecture,
possibility of approximating nonlinear functions,
insensitivity to the distortion of the network, and
inexact input data [8]-[14] [17].[20].In this paper
we present the evaluation of flux and torque using
the three stator currents is the voltage of input
inverter, and Fuzzy logic and artificial neural
network has been devised having as inputs the
torque error, the stator flux error and the position
of the stator flux in which it lies, and as output the
voltage space vector to be generate by the
inverter[8]-[13],[17].The ANN then replaces the
switching table’. The theoretical Principle,
numerical simulation procedures and the results of
these methods are discussed and compared with
conventional DTC (C_DTC).
induction motor drive. A voltage source inverter
(VSI) supplies the motor and it is possible to
control directly the stator flux and the
electromagnetic torque by the selection of
optimum inverter switching modes [1]-[4].
2.
DIRECT TORQUE CONTROL WITH
TWO-LEVEL INVERTER
Fig. 1 shows the schematic of The basic
functional blocks used to implement the DTC of
35
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application of the transformation given by (5) and
(6), [1] :
⎧
⎪ I Sα =
⎪
⎨
⎪I
=
⎪⎩ S β
2
Isa
3
1
(Isb − Isc
2
(5)
)
⎧
2 ⎛
1
⎞
U 0 ⎜ C1 − (C2 +C 3 ) ⎟
⎪VSα =
⎪
3 ⎝
2
⎠
⎨
⎪V = 1 U (C −C )
Sβ
0
2
3
2
⎩⎪
(6)
The components of the stator flux (ϕsα, ϕsβ) given
by (7).
Figure 1. Basic direct torque control scheme for
ac motor drives
t
⎧
⎪ϕ S α = ∫ (V S α − R S I S α ) dt
⎪
0
⎨
t
⎪ϕ = (V − R I ) dt
S Sβ
⎪ Sβ ∫ Sβ
0
⎩
2.1. Vector Model of Inverter Output Voltage
In the PWM voltage source inverters, considering
the combinations of the states of switching
functions inverter switching state functions
(C1,C2,C3) which can take either 1 or 0, the
voltage vector becomes:
The stator flux linkage phase is given by (8).
ϕ S = ϕ 2α + ϕ 2β
S
Vs =
4π
2π
j
j
⎤
2 ⎡
U 0 ⎢C1 + C 2 e 3 + C3e 3 ⎥
3 ⎣
⎦
(7)
(1)
(8)
S
The electromagnetic couple be obtained starting
from the estimated sizes of flux (ϕsα,ϕsβ and
calculated sizes of the current, Isα Isβ)
Eight switching combinations can be taken
according to the above relationship: two zero
voltage vectors and six non-zero voltage vectors
show by Fig.2 [1][2].
Γem = p (ϕ sα I sβ − ϕ sβ I sα )
(9)
The stator resistance Rs can be assumed constant
during a large number of converter switching
periods Te. The voltage vector applied to the
induction motor remains also constant one period
Te. Therefore, resolving first equation of system
leads to:
ϕS =
t
∫ (V
s
− R s I s ) dt
(10)
0
Figure 2. Partition of the αβ plane into 6 angular
sectors
ϕ S (t ) ≈ ϕ S 0 + V Te
S
(11)
In equation (11); φs0 stands for the initial stator
flux condition. This equation shows that when the
term RsIs can be neglected, (in high speed
operating condition for example), the extremity of
stator flux vector Vs. Furthermore, the
2.2. Stator Flux and Torque Estimation
The components of the current (Isα, Isβ), and
stator voltage (Vsα, Vsβ) are obtained by the
36
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maintain the end of the vector flux, in a circular
ring. The switching table proposed by Takahashi
[1], as given by Table1.
instantaneous flux speed is only governed by
voltage vector amplitude [1][4].
In fact, we have
dϕ S
≈V
dt
S
the following
Fig.3 Established for the case Vs=V3.
Table1. The switching table for DTC basis
3.
DTC BASED FUZZY LOGIC
The principal of direct torque control using
fuzzy logic (FDTC). The fuzzy controller is
designed to have three fuzzy state Variables and
one control variable for achieving direct torque
Control of the induction machine[8][9], there are
three variable input fuzzy logic controllers, the
stator flux error, electromagnetic torque error, and
angle of flux stator respectively the output it is the
voltage space vector.
Figure 3. An example for flux deviation
Therefore, by adequate voltage vector selection
we can increase or decrease the stator flux
amplitude and phase to obtain the required
performances. The deviation obtained at the end
of the switching period Te can be approached by
the first order Taylor Seri as below.
The radial component (component of flux) of the
vector of tension acts on the amplitude of the
vector flux and its tangential component
(component of the torque) on the position of the
vector flux. By choosing a suitable sequence of
the vectors of tension, one can force the end of the
vector flux to follow a desired trajectory. To
function with a module of practically constant
flux ϕs, it is enough to choose an almost circular
trajectory for the end of the vector flux. That is
not possible that if the period of control is very
weak for you in front of the period of rotation of
flux [1], [3] [10].
Flux Linkage Errors
The errors of flux linkage is related value of
stator’s flux ϕs* and real value of stator’s ϕs*, they
are subject to equation
∆ϕ= ϕs* -ϕs
(12)
We use the three following linguistic terms:
negative value, zero value and positive value
denoted respectively N, Z and P. Three fuzzy sets
are then defined by the delta and trapezoidal
membership functions as given by Fig.4,[9][10].
Electromagnetic Torque Errors
Error of torque Ete is related to desired torque
value T∗e and real torque value Te, they are subject
to equation (13)
2.3. Switching Table
When flux is in zone I, the vectors Vi+1 or Vi-1 are
selected to increase the amplitude of flux, and Vi+2
or Vi-2 to decrease it. What shows that the choice
of the vector tension depends on the sign of the
error of flux, independently of its amplitude [1].
This explains why the exit of the corrector of flux
can be a Boolean variable. One adds a band of
hysteresis around zero to avoid useless
commutations when the error of flux is very small,
[1] [2]. Indeed, with this type of corrector in spite
of his simplicity, one can easily control and
∆Γ =T∗e-Te
(13)
rules may be described by language variable, i, e.
Positive Large (LP), Positive Small (PS),
Negative Small (NS), and Negative Large (NL),
their membership function’s distribution is shown
as Fig.5, [9],[10] [14],
Angle of Flux Linkage θS
37
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The angle of flux linkage θsis an angle between
stator’s flux ϕs and a reference axis is defined by
equation (14):
θ s = ar tan
ϕ βs
ϕ αs
(14)
Figure 7. Membership functions for flux
error
in equation 3 ϕsα and ϕsβ are the component of
flux linkage ϕs in the plan (α,β) on the basis of
voltage vector shown as Fig.2, fuzzy variable may
be described by 12 language value (θ1→θ12),it’s
the membership function’s distribution is shown
Fig.6 [9].
5.2. The Control Variable
Each control rule can be described using the state
variables∆ϕ, ∆Γ θs and U. The ith rule Ri can be
written as:
3.4. Voltage Vectors Ui
For the voltage vectors Ui(i=0-6), the membership
distribution function of Ui is given by Fig.7.
Ri : if ∆ϕ, is Ai, ∆Γ is Bi and θs is Ci then n is
Ni
The membership functions of variables A, B, C
and N are given by µA, µB, µC and µN respectively.
The weighting factor αi for ith rule can be written
as [9][10][13].
α i= min(µAi (∆ϕ), µBi (∆Γ), µCi (∆θs )) (15)
Figure 4. Membership functions for flux
error
By fuzzy reasoning, Mamdani's minimum
procedure [9]
gives :
µ’Ni(n)=min(αi, (∆Γ),µNi(n)) (16)
The membership function µN of the output n is
point given by:
180
µ N (n) = max(αi, µ Ni' (n))
Figure 5. Membership functions for flux
error
i =1
(17)
7
µ Nout (n) = max( µ Nout (n))
i =1
(18)
According to the all rules and mamdani’s organ,
and all the variable membership function, a fuzzy
control have 180 table can gain, as shown table2
[9], The fuzzy control table be queried in real time,
deposited
the
table
into
memory
of
microcomputer.
Figure 6. Membership functions for flux
error
38
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4. DTC BASED NEURAL NETWORK
Principles of Artificial Neural Networks
Artificial neural networks use a dense
interconnection of
computing nodes to
approximate nonlinear functions [19][20].Each
node constitutes a neuron and performs the
multiplication of its input signals by constant
weights, sums up the results and maps the sum to
a nonlinear activation function g; the result is then
transferred to its output. A feed forward ANN is
organized in layers: an input layer, one or more
hidden layers and an output layer. A MLP consists
of an input layer, several hidden layers, and an
output layer [15]-[22]. Node i, also called a
neuron, in a MLP network is shown in Fig.8. It
includes a summer and a nonlinear activation
function g.
Fig 8. A multilayer perceptron network with one hidden
layer.
.
The inputs xk, k = 1...K to the neuron are
multiplied by weights wki and summed up together
with the constant bias term θi. The resulting i n is
the input to the activation function g. The
activation function was originally chosen to be a
relay function, but for mathematical convenience
a hyberbolic tangent (tanh) or a sigmoid function
are most commonly used [15] [22].
The mathematical model of a neuron is given by
(19):
⎛N
⎞
yi = gi = g⎜ ∑ w j i .x j + θi ⎟ (19)
⎝ i=1
⎠
4.2. Simulation Model and Structure of DTC
System Based ANN
The ANN is trained by a learning algorithm
which performs the adaptation of weights of the
network iteratively until the error between target
vectors and the output of the ANN is less than an
error goal. The most popular learning algorithm
for multilayer networks is the backpropagation
algorithm and its variants [l9]. The latter is
implemented by many ANN software packages
such as the neural network toolbox from
MATLAB [19] [20].
In the case presented in this paper the DTC
control strategy shown on table I has been
implemented. Neural network has been devised
having as inputs the torque error, the stator flux
error and the position of the stator flux, and as
output the voltage space vector to be generate by
the inverter [17]. The ANN block then replaces
the switching table selector block of Fig.9.
Table 2. Fuzzy logic rules
39
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Fig 11. Simulink block for ANN switching table
The block neural network content two layer 1 and
2 show Fig.12
Fig 9. Basic direct torque control scheme based ANN
Fig 12. Block neural network
To create the block ANN switching table we
passed by this program Matlab.
Where the Layer1 and Layer2 given by Fig.13
%P inputs
(E_TORQUE,E_FLUX,E_POSITION)
p=[0 0 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1;0
0 0 0 0 0 1 1 1 1 1 1 0 0 0 0 0 0 1 1 1 1 1 1;1 2 3 4
5 6 1 2 3 4 5 6 1 2 3 4 5 6 1 2 3 4 5 6];
% vector output of state
Sa,Sb,Sc.
t=[0 1 0 1 0 1 0 0 0 1 1 1 1 0 1 0 1 0 1 0 0 0 1 1;0
1 0 1 0 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 1 0 0 0;0 1 0 1
0 1 0 1 1 1 0 0 1 0 1 0 1 0 0 0 1 1 1 0];
net10 = newff([0 1;0 1;1 6],[10 3],{'tansig'
'purelin'});
net10.trainParam.epochs = 1000;
net10.trainParam.goal=0;
net10 = train(net10,p,t);
Y = sim(net10,p); e=t-Y; plot(p,t,p,Y,'o')
Fig 13. Block Layer1 and Layer2
The training ANN is given by Fig.10
6. INTERPRETATION RESULTS
To study the performance of the fuzzy logic
and neural network switching table with direct
torque control strategy, the simulation of the
system was conducted using SIMULINK and
Fuzzy Logic Toolbox.
Simulation results for a DTC system when
controlling the induction machine is following
parameters:
Fig 10. The training ANN
In Matlab command we generate the Simulink
block ANN of switching table by ‘’gensim
(net10)’’ given this model show Fig11
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PN ＝ 3KW ， Vn ＝ 230V ， fN ＝ 60Hz ， Rs ＝
8. SIMULATION RESULTS
2.89Ω，Rr＝2.39Ω，P＝2，Ls＝Lr＝0.225H，
Lm＝0.214H，J＝0.005kgm2. 3KW.
ELECTRPMAGNETIC TORQUE
9
The Sampling period of the system is 50µs.
To compare with C_DTC, FLDTC and
ANN_DTC for IM are simulated. In two cases,
the dynamic responses of speed, flux, torque and
stator current for the starting process with
[5→7→3] Nm load torque applied and a constant
command flux of 0.6Wbs are shown in Figure
from 14to 17 respectively. Figs.14 (a, b and c)
show the response of electric torque of the
C_DTC, FL_DTC and ANN_DTC respectively. It
can be seen that the ripple in torque with FL_DTC
and ANN_DTC control is less than 0.3 Nm and
with conventional direct torque control the ripple
is about 2 Nm at the same operating conditions.
Figs.15 (a, b and c) show the response of stator
flux magnitude of the C_DTC, FLDTC and
ANN_DTC respectively. By FLDTC and
ANN_DTC technique shown Fig15 (b and c), the
stator flux are the fast response in transient state
and the ripple in steady state is reduced
remarkably compared with conventional DTC, the
flux changes through big oscillation and the
torque ripple is bigger in C_DTC shown Fig15a.
Fig16 (a, b and c), It can be noticed that stator
flux vector describes a trajectory almost circular.
Figs .17(b and c) show the steady state current
response of the FLDTC and ANN_DTC has
negligible ripple in stator current and a nearly
sinusoidal wave form while as with conventional
DTC the stator current has considerably very high
ripple.
Telm
Tref
8
7
Telm Tref[N.m]
6
5
4
3
2
1
0
0
0.05
0.1
0.15
0.2
Temps[s]
0.25
0.3
0.35
0.4
Fig.14a. Electromagnetic torque
Response C DTC
ELECTRPMAGNETIC TORQUE
8
Telm
Tref
7
6
Telm Tref[N.m]
5
4
3
2
1
0
-1
0
0.05
0.1
0.15
0.2
Temps[s]
0.25
0.3
0.35
0.4
0.35
0.4
Fig.14b. Electromagnetic torque
Response FL DTC
ELECTRPMAGNETIC TORQUE
7. CONCLUSION
8
7
In this paper a FLDTC and ANN_DTC of
induction machine have been proposed. An
improved torque and flux response was achieved
with the FLDTC and ANN_DTC than the
conventional DTC. The performance has been
tested by simulations. Also, a
command flux optimization scheme has been
proposed to reduce the torque ripple. The
optimization was tested using simulation. The
results show a reasonable improvement by flux
optimization. The main improvements shown are:
• Reduction of torque and current ripples in
transient and steady state response.
• No flux droppings caused by sector changes
circular trajectory.
• Fast stator flux response in transient state.
Telm Tref[N.m]
6
5
4
3
2
1
0
0
0.05
0.1
0.15
0.2
Temps[s]
0.25
0.3
Fig.14c. Electromagnetic torque Response
ANN DTC
41
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Direct and Quadratic Stator Flux
0.8
STATOR FLUX MAGNITUDE
0.7
Phis
Phiref
0.6
0.6
0.4
Phisq[Wb]
0.2
0.4
0
-0.2
0.3
-0.4
0.2
-0.6
0.1
-0.8
-0.8
0
0
0.05
0.1
0.15
0.2
TEMPS[s]
0.25
0.3
0.35
-0.6
-0.4
-0.2
0.4
0
Phisd[Wb]
0.2
0.4
0.6
0.8
Fig.16a. Direct and quadratic stator
flux C_DTC
Fig.15a. The stator flux Magnitude C_DTC
Direct and Quadratic Stator Flux
0.8
STATOR FLUX MAGNITUDE
0.7
Phis
Phiref
0.6
0.6
0.4
0.5
Phisq[Wb]
0.2
Phis[Wb]
0.4
0
-0.2
0.3
-0.4
0.2
-0.6
0.1
-0.8
-0.8
0
0
0.05
0.1
0.15
0.2
Temps[s]
0.25
0.3
0.35
-0.6
-0.4
-0.2
0.4
0
Phisd[Wb]
0.2
0.4
0.6
0.8
0.6
0.8
Fig.16b. Direct and quadratic stator
flux FL DTC
Fig.15b. The stator flux Magnitude
FL DTC
Direct and Quadratic Stator Flux
0.8
STATOR FLUX MAGNITUDE
0.7
Phis
Phiref
0.6
0.6
0.4
0.5
Phisq[Wb]
0.2
0.4
Phis[Wb]
Fs[Wb]
0.5
0
-0.2
0.3
-0.4
0.2
-0.6
0.1
-0.8
-0.8
0
0
0.05
0.1
0.15
0.2
Temps[s]
0.25
0.3
0.35
0.4
-0.6
-0.4
-0.2
0
Phisd[Wb]
0.2
0.4
Fig.16c. Direct and quadratic stator flux
ANN DTC
Fig.15c. the stator flux Magnitude
ANN DTC
42
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